Question

if AM and GM of two positive numbers a and b are 10 and 8, then find the numbers
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Answer 1

Answer:

according to question

a+b= 20

a.b=64

therefore

a.(20-a)=64

20a-a²=64

or

a²-20a+64=0

a²-16a-4a+64=0

a(a-16)-4(a-16)=0

(a-16)(a-4)=0

therefore a= 16or 4

b= 4or 16

Step-by-step explanation:

please mark it as BRAINLIST.

Answer 2

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⇒AM = $\frac{a + b}{2}$

⇒ GM = √ab

Given AM = 10, GM = 8.

⇒ $\frac{a + b}{2}$ = 10

⇒ a + b = 20

⇒ a = 20–b

⇒ $\sqrt{(20 - b)b}$

⇒ 20b – b²= 64

⇒ b² – 20b + 64 = 0

⇒ b²– 16b – 4b + 64 = 0

⇒ b(b – 16) – 4(b – 16) = 0

⇒ b = 4 or b = 16

⇒ If b = 4

then a = 16

⇒ If b = 16

then a = 4.

Hence, the numbers are 4 and 16